Related papers: Synchronization in abstract mean field models
We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.
In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms''…
We generalize the strategy, we recently introduced to prove the existence of the thermodynamic limit for the Sherrington-Kirkpatrick and p-spin models, to a wider class of mean field spin glass systems, including models with multi-component…
We devise a field theoretical formalism for a microscopic theory of nucleation processes and phase coexistence in finite dimensional glassy systems. We study disordered $p$-spin models with large but finite range of interaction. We work in…
Mixed monotone systems form an important class of nonlinear systems that have recently received attention in the abstraction-based control design area. Slightly different definitions exist in the literature, and it remains a challenge to…
Coupled cell systems are dynamical systems associated to a network and synchrony subspaces, given by balanced colorings of the network, are invariant subspaces for every coupled cell systems associated to that network. Golubitsky and…
We study the effect of introducing separable quenched disorder on a non-equilibrium mean-field spin model exhibiting a phase transition to an oscillating state in the absence of disorder, due to non-reciprocal interactions. In the…
Inspired by distributed applications that use consensus or other agreement protocols for global coordination, we define a new computational model for parameterized systems that is based on a general global synchronization primitive and…
We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…
We investigate quantum synchronization phenomenon within the complex network constituted by coupled optomechanical systems and prove the unknown identical quantum states can be shared or distributed in the quantum network even though the…
We study the convergence problem of mean-field control theory in the presence of state constraints and non-degenerate idiosyncratic noise. Our main result is the convergence of the value functions associated to stochastic control problems…
We define am axiomatic timeless framework for asynchronous distributed systems, together with well-formedness and consistency axioms, which unifies and generalizes the expressive power of current approaches. 1) It combines classic…
We study numerically a disordered model that interpolates among the Sherrington-Kirkpatrick mean field model and the three dimensional Edwards-Anderson spin glass. We find that averages over the disorder of powers of the overlap and of the…
This work introduces the phenomenon of Collective Almost Synchronization (CAS), which describes a universal way of how patterns can appear in complex networks even for small coupling strengths. The CAS phenomenon appears due to the…
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…
We discuss a class of explicitly solvable mean field type control problems/mean field games with a clear economic interpretation. More precisely, we consider long term average impulse control problems with underlying general one-dimensional…
We review recent statistical mechanical approaches to multimode laser theory. The theory has proved very effective to describe standard lasers. We refer of the mean field theory for passive mode locking and developments based on Monte Carlo…
We exhibit new conditions under which a primitive automaton is synchronizing. In particular, we show that the primitivity of an automaton forces its synchronizability whenever the automaton has either a letter of defect 1 or a word of rank…
Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean…
We introduce a mean field spin glass model with gaussian distribuited spins and pairwise interactions, whose couplings are drawn randomly from a normal gaussian distribution too. We completely control the main thermodynamical properties of…